In their physical proposal for quantization, Gukov-Witten suggested that, given a symplectic manifold M with a complexification X, the A-model morphism spaces Hom(Bcc, Bcc) and Hom(B,Bcc) should recover holomorphic deformation quantization of X and geometric quantization of M respectively. Here, Bcc is a canonical coisotropic A-brane on X and B is a Lagrangian A-brane supported on M. Assuming M is spin and K ̈ahler with a prequantum line bundle L, Chan-Leung-Li constructed a subsheaf Oqu of smooth functions on M with a non-formal star product and a left Oqu-module structure on the sheaf of holomorphic sections of L ⊗ In this talk, I will discuss the relation between (holomorphic) deformation quantizations of M and X so as to verify that Chan-Leung-Li's work provides a mathematical realization of the action of Hom(Bcc,Bcc) on Hom(B,Bcc). I will also explain my recent work - the construction of a Oqu-Oqu-bimodule structure on the sheaf of smooth sections of L⊗2 realizing the actions of Hom(Bcc,Bcc) and Hom(Bcc,Bcc) on Hom(Bcc,Bcc), which is related to the analytic geometric Langlands program.